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A poisson variable satisfies P( x = 1) = P( x = 2) Find P( x = 5).

A poisson variable satisfies P( x = 1) = P( x = 2) Find P( x = 5).

Grade:upto college level

1 Answers

Latika Leekha
askIITians Faculty 165 Points
7 years ago
A random variable X is said to have a poisson distribution with parameter ‘t’ if
P(X, t) = e-t tx/ x!
Now, P(X = 1) = e-t . t/ 1! = te-t
P(X = 2) = e-t. t2/ 2! = t2e-t/ 2
Given that P(X = 1) = P(X = 2)
Hence, this implies te-t = t2e-t/ 2
This gives t = t2/2
Hence, we have t = 2.
Now, P(X = 5) = e-2. 25/ 5!
= 32e-2/120.
This is the required answer.
Thanks & Regards
Latika Leekha
askIITians Faculty

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